A 'microfluidic pinball' for on-chip generation of Layer-by-Layer polyelectrolyte microcapsules

Inspired by the game of "pinball" where rolling metal balls are guided by obstacles, here we describe a novel microfluidic technique which utilizes micropillars in a flow channel to continuously generate, encapsulate and guide Layer-by-Layer (LbL) polyelectrolyte microcapsules. Droplet-based microfluidic techniques were exploited to generate oil droplets which were smoothly guided along a row of micropillars to repeatedly travel through three parallel laminar streams consisting of two polymers and a washing solution. Devices were prototyped in PDMS and generated highly monodisperse and stable 45±2 μm sized polyelectrolyte microcapsules. A total of six layers of hydrogen bonded polyelectrolytes (3 bi-layers) were adsorbed on each droplet within <3 minutes and a fluorescent intensity measurement confirmed polymer film deposition. AFM analysis revealed the thickness of each polymer layer to be approx. 2.8 nm. Our design approach not only provides a faster and more efficient alternative to conventional LbL deposition techniques, but also achieves the highest number of polyelectrolyte multilayers (PEMs) reported thus far using microfluidics. Additionally, with our design, a larger number of PEMs can be deposited without adding any extra operational or interfacial complexities (e.g. syringe pumps) which are a necessity in most other designs. Based on the aforementioned advantages of our device, it may be developed into a great tool for drug encapsulation, or to create capsules for biosensing where deposition of thin nanofilms with controlled interfacial properties is highly required.     

Characterization of a microscale cyclical electrical field flow fractionation system

A microscale cyclical electrical field flow fractionation (CyElFFF) channel is characterized with regard to the effect of various operating parameters and comparison made to recent theoretical developments. Challenges associated with various operating conditions are reported along with some of the optimized operating parameters. The effect of retention wall choice, an offset voltage, relaxation steps, and flow rates, along with the basic operating parameters of voltage, frequency, and electrophoretic mobility are reported. Retention of polystyrene nanoparticle standards is accomplished and the first separations using this technique in a microscale system are also demonstrated. Relaxation steps and offset voltages are found to be effective in eliminating early peaks and in improving plate heights. Plate heights were also found to decrease with increasing flow rates, which is the opposite of the behavior seen in most existing chromatographic systems. The experimental results are compared to the analytical and empirical models of CyElFFF and found to be compatible. Suggestions are made for improving the separation and analysis methods used with CyElFFF.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.     

库仑加线性位基态解析解

应用新发展的单一轨迹积分方法求解库仑加线性位的基态量子波函数,得到基态能量和波函数的一般解析表达式,并讨论了解的收敛性.应用此方法讨论了重夸克偶素系统.